1. Field of the Invention
The present invention provides a method and apparatus for determining the three-dimensional positions of objects based on two-dimensional (azimuth and elevation) coordinates from two separate passive sensors.
2. Description of the Related Art
Determining the three-dimensional position of a target object such as an aircraft or missile using active radar is a straightforward process. Azimuth and elevation coordinates (two dimensions) are provided by the radar's antenna scanning system. The range to the object, which constitutes the third coordinate, is provided by measuring the time-of-flight of radio frequency pulses transmitted toward and reflected back from the object. The three-dimensional coordinates of the object relative to a particular reference point, such as the center of the earth, may be easily derived using simple coordinate transformations since the position of the radar relative to the reference point is known.
However, tracking of objects such as hostile missiles using data from sensors mounted on orbiting satellites is much more difficult, since these sensors are conventionally passive and provide only relative azimuth and elevation coordinates. Lines-of-sight from two or more sensors can be triangulated to derive a third coordinate for target position determination. However, where a significant number of objects are being tracked, multiple lines-of-sight intersect at points where no objects actually exist. A method must therefore be provided to eliminate the false intersections from further consideration and match the lines-of-sight from the respective sensors to the individual objects.
U.S. Pat. No. 4,806,936, entitled "METHOD OF DETERMINING THE POSITION OF MULTIPLE TARGETS USING BEARING-ONLY SENSORS" issued Feb. 21, 1989, to Patrick R. Williams, assigned to the Hughes. Aircraft Company, the assignee of the patent as well as the present application, described a "deghosting algorithm". The positions of a plurality of targets are located using three or more sensors such as jammed radars which sense only the azimuth or bearing angle to the targets. The intersecting bearing lines form triangles representing both true targets and false or "ghost" targets. The false target triangles are separated from the true target triangles by analyzing the size and position of each triangle. Bearing data defining the triangles is first ordered, and then sequentially examined in a manner such that a first group of false targets is eliminated from consideration. The bearing data defining the remaining triangles is processed through coarse and fine gates to eliminate the second and third groups of false targets. A fourth group of false targets is eliminated by using a global maximum likelihood procedure, in which a likelihood function is maximized through the use of discrete optimization techniques.
In the worst case using the deghosting method for n targets, n.sup.3 candidate target locations must be searched in order to determine the actual locations of the objects. In addition, the search algorithm utilizes an exhaustive search procedure which has an overall complexity of n.sup.2n for n targets. In a realistic defense scenario in which hundreds or more missiles must be tracked simultaneously, such a search using even the most current computer technology would require a length of time greatly in excess of the time-of-flight of the missiles.